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a permutation of coefficients of trinomials , f(x) \geq g(x) for all real x?

Source: Tuymaada Junior 2007 p2

May 12, 2019

algebratrinomialquadratic trinomial

Problem Statement

Two quadratic trinomials

f (x)

and

g (x)

differ from each other only by a permutation of coefficients. Could it be that

f (x) \geq g (x)

for all real

x